Considering, that my current Castoff is Gold/Blue (though I feel like it actually should be Gold/Blue/Indigo, though there is no such position) I have a a general feeling, how to get Gold (as it's ridiculously overpresent in the game), but how to balance out the Red, without scewering the Gold Tide, I have no idea.

I finished the game twice, and twice ended up with a combination of Gold and Blue (Gold/Blue first, Blue/Gold second...), so I don't really know if it's my playstyle or if those two Tides are well over-represented. So sorry can't help you much getting Red... although I'll try another playthrough as a Glaive, maybe this time I'll get more Red

From my understanding (but I might be wrong), you only ever gain points toward a Tide by selecting answers/doing things, answer X will give +5 Red, answer Y +8 Gold, ... And then the score of your Tides are compared, if one is sufficiently ahead of all others you get a "pure Tide", else you get the top two of your Tides. But it would be nice to have a more detailed answer from developers (or someone who reverse engineered the code, or whatever :p).

But what if you have three Tides tied (or one dominant and two close behind), for example? How will the game determine which two are dominant?

If you've one dominant and two close behind, you'll only get the dominant Tide (so, like it happened to me once, I was Blue/Gold, then selected a Silver answer, and went to pure Blue, since the Silver raised close enough to the Gold). You need a sufficient (but I don't know how big) gap between the #2 and the #3 to get two Tides.

What happens if you no dominating Tide at all, that I don't know. Initially it was planned for a Grey Legacy when you have no dominant Tide at all, but I don't know if that was implemented.